`int 1/(sqrt(x)-root3(x)) dx` Use substitution and partial fractions to find the indefinite integral

Expert Answers

An illustration of the letter 'A' in a speech bubbles


Apply integral substitution:`u=x^(1/6)`









Take the constant out,


Integrand is an inproper rational function as degree of numerator is more than the degree of the denominator,

So let's carry out the division,



Apply the sum rule,


Apply the power rule and the common integer:`int1/xdx=ln|x|`


Substitute back `u=x^(1/6)`

and add a constant C to the solution,





Approved by eNotes Editorial Team